Flavian Amphiteatre and Olympic games are are economic doomsday weapons. Olympic games provides minor bonuses in exchange for making a city utterly useless for military production. Flavian Amphiteatre is a 'I win' button for every other Civ. FA is made for when an empire is so big and sprawling that it needs to institute the dreaded 'Bread and Circuses' policy. In short, needing to build the FA means you have built so improbably many cities over what your economy can handle your empire is going to stagnate to death or collapse inot civil war endlessly. In short, if your not a massively over expanded Spiritual Civ then never, Never, NEVER EVER build that thing. Historically building that thing means you fail at running a Civ Forever. Just ask the Romans.